Performance Evaluation of D SFC GM

In this section, we compare the performance of D SFC AM and D SFC GM algorithms with Topological Sorting (D SFC TS) algorithm [91]. In D SFC TS, the two processes of SFC design and mapping are conducted sequentially. The basic idea of D SFC TS is to first construct a chain by exploiting the topological sorting method [105]. Then, D SFC TS maps the constructed chain onto the substrate network. By using topological sorting method, D SFC TS guarantees the dependence relationships among the VNF nodes are not violated in the constructed chain. The output of topological sorting is a linearly ordered vertices of a Directed Acyclic Graph (DAG). Once the chain constructed by the topological sorting is fixed, one can treat the constructed chain as a network and call the traditional virtual network embedding algorithms to conduct the node mapping and link mapping. Here, we use the traditional scheme that gives priorities to substrate nodes with larger available CPU and shorter routing paths [64, 107, 108].

We use a 28-node US Backbone network [109] as the substrate IP or optical network. Unless otherwise specified, the available computing resources of substrate nodes is in the range of [5,35]; the offered functionality for each substrate node is randomly generated; the available bandwidth (or number of subcarriers) for each substrate link varies from 5 to 45;

and there is no wavelength conversion in the substrate optical networks. Similarly, unless otherwise specified, the number of VNF nodes (N) in an NFV service request (N SR) is set in the range of [3,8]; the dependent constraints among the VNF nodes are randomly generated;

each VNF node requests a computing demand in the range of [5,25], and eachN SRrequests

the bandwidth (or number of subcarriers) within the range of [5,25]. The NSR is randomly

generated and we collect the average bandwidth (spectrum) consumption for embedding a large number of NSRs over 100 different substrate networks, which are denoted as ”Average BW (Spectrum) Consumption” in the following figures. We compare and analyze how the number of VNF nodes, bandwidth and computing demand in an NSR impact the performance from the proposed D SFC GM, D SFC AM and D SFC TS algorithms.

The impact of optical constraints

Figure 5.5 shows the impact of optical network constraints (spectrum continuity and consecutiveness). Here, we compare the performance of the three algorithms for two cases where wavelength conversion is available in the substrate network (i.e., D SFC GM Conv) and wavelength conversion is not provided (i.e., D SFC GM NO Conv). For this experiment, substrate resources are limited as mentioned earlier. In Figure 5.5, the X-axis is the number of VNF nodes in the request and the Y-axis is the average spectrum consumption. As one can see, for all three algorithms, the average spectrum consumption is the highest for the case that no wavelength conversion is available in the substrate network, whereas both spectrum continuity and consecutiveness must be satisfied. When the wavelength conversion is available only consecutiveness constraint should be satisfied. Hence, shorter paths can be found between the nodes on the SFP which results in less spectrum consumption.

The impact of NFV service request size

To study the impact of N SR size, we set each substrate node with unlimited com-

puting resources and set each substrate link with unlimited bandwidth (or number of sub-

Figure (5.5) Impact of optical constraints

nodes in the N SR varies from 3 to 8. We set the substrate network as IP network to

obtain the results in Figure 5.6(a) and set the substrate network as optical network in Fig- ure 5.6(b). Figure 5.6(a) and 5.6(b) show the average bandwidth (spectrum) consumption

when increasing the number of VNF nodes in the N SR. As one can see, for all three

algorithms, the average bandwidth (spectrum) consumption increases with the number of VNF nodes in the NSR. Both the proposed D SFC GM (D SFC GM NO Conv for optical) and D SFC AM (D SFC AM NO Conv for optical) algorithms significantly outperform the D SFC TS (D SFC TS NO Conv for optical) in IP (optical) substrate networks. This is because the proposed techniques including dependence sorting, independent grouping and adaptive mapping enable D SFC GM and D SFC AM to design better SFCs. Particularly, here, the substrate networks have abundant CPU and bandwidth (or number of subcarriers) resources, which makes the processes of VNF node and link mapping in all three algorithms to follow similar behavior. As a result, a better SFC design will require less bandwidth (or number of subcarriers) along the Service Function Path (SFP) in the substrate network. Furthermore, the D SFC GM algorithm has slightly better results than the D SFC AM al- gorithm due to the Tetragon Remapping technique in D SFC GM. The process of Tetragon

Remapping in D SFC GM can further optimize the VNF link mapping by identifying closer substrate nodes that the VNF nodes can be relocated to.

(a) Substrate IP networks

(b) Substrate optical networks

The impact of NFV service request bandwidth

When investigating the impact of NSR bandwidth, we set substrate resource limited as

mentioned earlier. Each N SR is randomly generated with 6 VNF nodes and 5 dependen-

cies and the requested bandwidth for the N SR varies from 5 to 25. In Figure 5.7(a), the

y-axis denotes the average bandwidth consumption and the x-axis represents the requested bandwidth for the NFV service request. One can see that when the requested bandwidth increases, the average bandwidth consumption of three algorithms increases as well. In par- ticular, D SFC AM outperforms D SFC TS because the D SFC AM algorithm can jointly optimize the chain design and VNF node/link mapping processes by applying dependence sorting, independent grouping and adaptive mapping techniques. As for D SFC GM algo- rithm, it outperforms D SFC AM as D SFC GM employs the Tetragon Remapping technique to avoid the shortview mapping in D SFC AM. It is worthy noting that when the NSR band- width request is higher than 25, due to the lack of available links with enough bandwidth, there is not many alternative physical paths for D SFC embedding and all three algorithms converging to the similar performance. The results from substrate optical network in Fig- ure 5.7(b) further verify these observations.

The impact of CPU in the substrate network

Figure 5.8 shows the impact of the available CPU resources in the substrate nodes. To explore this impact, we set the range for available CPU resources of the substrate nodes as shown in Figure 5.8(a) and 5.8(b). We set the available bandwidth (or number of subcarriers)

of the substrate links as unlimited. EachN SRis randomly generated with 7 VNF nodes and

4 dependencies. The CPU requirement for all VNF nodes is 12 and the requested bandwidth (or number of subcarriers) for theN SRis set to 10. One can see that in both IP and optical networks, the average bandwidth (spectrum) consumption decreases when the range for available CPU resources increases. This is because more substrate nodes can satisfy the CPU requirement of the VNF nodes when the range for available CPU resources increases, leading

(a) Substrate IP networks

(b) Substrate optical networks

(a) Substrate IP networks

(b) Substrate optical networks

to possible shorter service function paths. Once again, the proposed D SFC GM yields better results than both D SFC AM and D SFC TS. In particular, D SFC GM outperforms D SFC AM and D SFC TS as much as 8% and 25%, respectively.

In this chapter, we introduced the problem of dependence-aware SFC design and map- ping. To solve the problem efficiently, we presented the D SFC AM which uses techniques such as dependence sorting, independent grouping and adaptive resource allocation to con- struct and map the chain onto the substrate network. To further optimize the bandwidth con- sumption in the substrate network, we presented D SFC GM which uses Tetragon Remap- ping technique to optimize the mapping for the constructed chain.